Question
How does a scale drawing that is larger than the object it represents relate to a geometric transformation?%0D%0AResponses%0D%0A%0D%0AIt is a dilation that moves the object to the right and down.%0D%0AIt is a dilation that moves the object to the right and down. - no response given%0D%0A%0D%0AIt is a dilation that decreases the size of the object.%0D%0AIt is a dilation that decreases the size of the object. - incorrect%0D%0A%0D%0AIt is a dilation that maintains the size of the object.%0D%0AIt is a dilation that maintains the size of the object. - no response given%0D%0A%0D%0AIt is a dilation that increases the size of the object.
Answers
GPT 3.5
It is a dilation that increases the size of the object.
explain how
GPT 3.5
A scale drawing is larger than the object it represents because it undergoes a geometric transformation called dilation. Dilation is a transformation that changes the size of an object without altering its shape or orientation.
In the case of a scale drawing, the object is enlarged by multiplying the lengths of its sides by a scale factor greater than 1. This means that every point of the object is moved away from the center of dilation, resulting in an increased size of the drawing.
To create a scale drawing, the center of dilation is chosen, and a scale factor is determined. The scale factor represents the ratio of the lengths of corresponding sides on the drawing and the actual object. For example, if the scale factor is 2, all the sides of the drawing will be twice as long as the corresponding sides on the actual object.
By applying the dilation transformation, the scale drawing is created, showcasing the object in a larger size while maintaining its proportions and shape. This is useful in many fields, such as architecture, engineering, and art, where it allows for accurate representations of objects on a smaller or more manageable scale.
In the case of a scale drawing, the object is enlarged by multiplying the lengths of its sides by a scale factor greater than 1. This means that every point of the object is moved away from the center of dilation, resulting in an increased size of the drawing.
To create a scale drawing, the center of dilation is chosen, and a scale factor is determined. The scale factor represents the ratio of the lengths of corresponding sides on the drawing and the actual object. For example, if the scale factor is 2, all the sides of the drawing will be twice as long as the corresponding sides on the actual object.
By applying the dilation transformation, the scale drawing is created, showcasing the object in a larger size while maintaining its proportions and shape. This is useful in many fields, such as architecture, engineering, and art, where it allows for accurate representations of objects on a smaller or more manageable scale.